Definition
Retrograde analysis is a strategy used in game theory to help make decisions early on to get the outcome you want. Applying this strategy to your decision making process can give you an edge against intimidating decisions you have to make.
Retrograde analysis is used for working backwards from the end of a game to the game’s starting state. This strategy involves tracing moves backwards in order to determine what moves led to a desired outcome. We can apply this way of thinking to our daily decisions. [1]
Who
Retrograde Analysis has applications in various mathematical and computational fields, such as: [2]
- Game theory: Retrograde Analysis is used to determine the optimal strategies for players in two-player perfect information games, such as chess, checkers, or tic-tac-toe.
- Combinatorial game theory: This technique is used to analyze the outcomes of combinatorial games, where the game positions can be described by mathematical structures, such as sets, graphs, or numbers.
- Computer science: Retrograde Analysis is used in the development of game-playing algorithms and AI systems, such as those used in chess or other strategy games.
- Optimization problems: Retrograde Analysis can be applied to solve certain optimization problems, where the goal is to find the optimal sequence of decisions or actions.
What
Retrograde Analysis is a powerful tool in mathematics and computer science, allowing for the systematic analysis and understanding of complex game-like situations and optimization problems.
Retrograde Analysis is a method for analyzing the outcome of a game by working backwards from the final positions or states of the game. It involves systematically determining the values of all possible game positions, starting from the terminal positions and working backwards towards the initial position.
The basic idea behind Retrograde Analysis is to determine the optimal strategy for a player by considering the possible responses of the opponent at each stage of the game. By working backwards from the final positions, the analysis can identify the optimal moves and strategies that lead to a win, a draw, or a loss for each player. [2]
Why
See Theoretical Knowledge Vs Practical Application.
How
Many of the References and Additional Reading websites and Videos will assist you with understanding and applying retrograde analysis.
As some professors say: “It is intuitively obvious to even the most casual observer.“
References
[1] Ho, Leon. 2023. “Retrograde Analysis: Work Backwards to Solve Problems Effectively.” LifeHack. February 13. https://www.lifehack.org/938420/retrograde-analysis.
[2] “Fast, Helpful AI Chat.” 2024. Poe. Assistant. Accessed June 15. https://poe.com/.
I used AI bots in this article to capture ideas that I could not develop on my own without more extensive research. I recall back in the 1990s attending presentations at conferences where the presenter was using crawler bots to gather information for their research. I am still experimenting with AI bots, and will continue to use them as needed to present ideas and concepts more clearly to the reader.
Additional Reading
“Applying Retrograde Analysis to Nine Men’s Morris” 2024. Semantic Scholar. Accessed August 1. https://www.semanticscholar.org/paper/Applying-Retrograde-Analysis-to-Nine-Men’s-Morris-Gasser-Eth/8b658eb4b3f22b1e9e2a70930eaf546ef5fb3f9e.
This paper presents results gained through retrograde analysis of Nine Men’s Morris. First, I describe some of the methods employed to accelerate the calculations, for example runlength encoding of the databases. Second, the results themselves are examined. While many human players intuitively regard Nine Men’s Morris as a rather simple, drawn game, my results seem to suggest otherwise. Some of the optimal play is clearly beyond human ability, sometimes requiring over 150 plies of seemingly random moves before a win is reached.
Butters, J., Henle, J. Baseball Retrograde Analysis. Math Intelligencer 40, 71–76 (2018). https://www.science.smith.edu/~jhenle/pleasingmath/retrobaseball.pdf (https://doi.org/10.1007/s00283-018-9846-y).
In a retrograde analysis puzzle you are presented with a position in a game and asked questions about what happened earlier. The term is almost exclusively applied to chess games and chess positions, but one can devise retrograde problems in many two-player games. It has never been applied, however to the eighteen-player game of baseball. Never, that is, until now.
“Chess Puzzles: Brilliant Math & Science Wiki.” 2024. Brilliant. Accessed August 1. https://brilliant.org/wiki/chess-puzzles/.
The field of chess puzzles is extremely diverse. It includes practical exercises to train one’s skills at the game, compositions to illustrate beauty and fun/themed challenges, recreational puzzles such as retrograde analysis, and mathematical puzzles related to chess. Solving these puzzles is a special case of combinatorial games.
G., Tim. 2024. “A Comparison: Retrograde Analysis and Working Backwards.” LinkedIn. June 26. https://www.linkedin.com/pulse/comparison-retrograde-analysis-working-backwards-tim-glenn-y5sne.
While retrograde analysis and the working backwards process share the concept of working backward from an endpoint, they are applied in different fields (chess and product development) and have different goals (solving puzzles and delivering customer value). The alignment between the two is to solve a problem.
“Retrograde Analysis: How to Solve Problems by Working Backwards.” 2018. Mayo Oshin. March 1. https://www.mayooshin.com/retrogade-analysis-working-backwards-maurice-ashley.
In my previous article, I wrote about the “Inversion” technique for solving difficult problems by working backwards.
Another powerful way to solve difficult problems is by using the chess “Retrograde Analysis” method. In simple terms, retrograde analysis is a technique used in chess to solve difficult chess problems by working backwards from known outcomes.
Videos
Imagine where you want to be someday. Now, how did you get there? Retrograde analysis is a style of problem solving where you work backwards from the endgame you want. It can help you win at chess — or solve a problem in real life. At TEDYouth 2012, chess grandmaster Maurice Ashley delves into his favorite strategy.
⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.
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Mathematical Mysteries 